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Entire solutions of the Allen-Cahn equation
Entire solutions of the Allen-Cahn equation
教师介绍

本讲教师:刘勇
所属学科:理科
人  气:712

课程介绍
Abstract:The Allen-Cahn equation arises in the gradient theory of phase transitions. In this lecture, we will discuss the existence and classification of the entire solutions of the Allen-Cahn type equations. As we will see, this type of equations are closely related to the theory of minimal surfaces and integrable systems, such as Toda system and elliptic sine-Gordon equation. It turns out that the structure of the solution space of the Allen-Cahn type equation is now better understood in dimension two than higher dimensions. For instance, the finite Morse index solutions of the elliptic sine-Gordon equation can be completed classified in dimension two. We will also mention some questions which remain to be answered in this area.

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